Write Lorentz force equation.

A particle moving in a magnetic field increases its velocity, then its radius of the circle

A positive, singly ionized atom of mass number $A_M$ is accelerated from rest by the voltage $192 V$. Thereafter, it enters a rectangular region of width $w$ with magnetic field $B_0=0.1 \hat{k}$ Tesla, as shown in the figure. The ion finally hits a detector at the distance $x$ below its starting trajectory.

[Given: Mass of neutron/proton $=(5 / 3) \times 10^{-27} kg$, charge of the electron $=1.6 \times 10^{-19} C$.]

Which of the following option($s$) is(are) correct?

$(A)$ The value of $x$ for $H^{+}$ion is $4 cm$.

$(B)$ The value of $x$ for an ion with $A_M=144$ is $48 cm$.

$(C)$ For detecting ions with $1 \leq A_M \leq 196$, the minimum height $\left(x_1-x_0\right)$ of the detector is $55 cm$.

$(D)$ The minimum width $w$ of the region of the magnetic field for detecting ions with $A_M=196$ is $56 cm$.

An electron enters a region where electrostatic field is $20\,N/C$ and magnetic field is $5\,T$. If electron passes undeflected through the region, then velocity of electron will be.....$m{s^{ - 1}}$

Two parallel beams of protons and electrons, carrying equal currents are fixed at a separation $d$. The protons and electrons move in opposite directions. $P$ is a point on a line joining the beams, at a distance $x$ from any one beam. The magnetic field at $P$ is $B$. If $B$ is plotted against $x$, which of the following best represents the resulting curve

Two particles $A$ and $B$ of masses ${m_A}$ and ${m_B}$ respectively and having the same charge are moving in a plane. A uniform magnetic field exists perpendicular to this plane. The speeds of the particles are ${v_A}$ and ${v_B}$ respectively, and the trajectories are as shown in the figure. Then